On rational maps from the product of two general curves

Yongnam Lee; Gian Pietro Pirola

On rational maps from the product of two general curves

Algebraic Geometry 2015-07-07 v2

Authors: Yongnam Lee , Gian Pietro Pirola

Abstract

This paper treats the dominant rational maps from the product of two very general curves to nonsingular projective surfaces. Combining the result by Bastianelli and Pirola, we prove that the product of two very general curves of genus $g\geq 7$ and $g'\geq 3$ does not admit dominant rational maps of degree $> 1$ if the image surface is non-ruled. We also treat the case of the 2-symmetric product of a curve.

Keywords

rational maps product of curves projective surfaces genus non-ruled surfaces symmetric product

Cite

@article{arxiv.1411.4263,
  title  = {On rational maps from the product of two general curves},
  author = {Yongnam Lee and Gian Pietro Pirola},
  journal= {arXiv preprint arXiv:1411.4263},
  year   = {2015}
}

Comments

13 pages; exposition improved; Ann. Sc. Norm. Super. Pisa Cl. Sci. (to appear)

On rational maps from the product of two general curves

Abstract

Keywords

Cite

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